Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.

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Extra Credit Project: The Spring Constant of Balls

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Potential, kinetic and spring energy of balls

This project may be done by teams of 1-2 individuals.

Your job in this assignment is to measure carefully the
energy which can be stored internally in different
types of balls.
You must choose at least 5 different types of ball;
for example, a tennis ball, a basketball, a soccer ball,
a super ball, a beach ball.

First, determine the mass and radius of each ball.
Make a guess at its composition, and draw a cross-section
of each ball showing its interior.

Second, drop each ball at least 3 times from a standard
height which is between 10 and 30 feet. You might use
a second-story window, or a tall ladder, or the roof of
a garage.
Measure carefully the distance between the drop point and the
ground (or other surface), and try to drop
all balls so that their center of mass starts at
the standard height.
Draw a diagram which shows the drop point, ground surface,
location of dropper and other persons.
Measure the height of each ball's
first bounce, and describe how you do so.

Calculate the potential energy of each ball at the drop
point, and the potential energy of each ball at the
peak of its first bounce.
What fraction of the initial energy was retained
through the first bounce?

Assume that each ball acts like a simple spring, with
a spring constant **k** such that the force required
to compress the radius of the ball by a distance **x** is equal to
**k*x**.
You should try to apply a known force (**F**) to each of your balls
(say, by placing an object of known mass on top of them)
and measure the resulting decrease in diameter (x).
Estimate the spring constant **k** for each ball.
What is the spring potential energy stored in the ball if you
squish it down so that its radius is **x** centimeters
smaller than the rest radius?

Assume that the gravitational potential energy recovered
in the first bounce is equal to the spring potential
energy stored in the ball when it hits the ground
after being dropped.
Determine as best you can the amount by which each ball
compresses as it bounces.
Make sure
that the units are correct!

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This page maintained by Michael Richmond.
Last modified Feb 9, 2000.
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Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.